Ultrametric approximations of a Drygas functional equation

Using the operatorial approach, we investigate the ultrametric approximate solutions of the following Drygas functional equation: Sigma(lambda epsilon Phi) f(x + lambda y _ a(lambda)) = vertical bar Phi vertical bar f(x) + Sigma(lambda epsilon Phi) f(lambda y), x, y epsilon E, where K is an ultrametric valued field of characteristic zero, E is a K-vector space, F is a complete ultrametric space over K, f epsilon F-E, Phi is a finite subgroup of the automorphism group of E with order vertical bar Phi vertical bar, and a(lambda) epsilon E for all lambda epsilon Phi.